{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T15:07:05Z","timestamp":1773500825760,"version":"3.50.1"},"reference-count":51,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,2,4]],"date-time":"2020-02-04T00:00:00Z","timestamp":1580774400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61901370"],"award-info":[{"award-number":["61901370"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Science and Technology Innovation Team for Talent Promotion Plan of Shaanxi Province","award":["2019TD-028"],"award-info":[{"award-number":["2019TD-028"]}]},{"name":"Shaanxi Science and Technology Achievements Promotion Project","award":["2018CG-007"],"award-info":[{"award-number":["2018CG-007"]}]},{"name":"the Local Special Project of Shaanxi Province Education Department","award":["18JC029"],"award-info":[{"award-number":["18JC029"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Wireless sensor network (WSN) nodes are devices with limited power, and rational utilization of node energy and prolonging the network lifetime are the main objectives of the WSN\u2019s routing protocol. However, irrational considerations of heterogeneity of node energy will lead to an energy imbalance between nodes in heterogeneous WSNs (HWSNs). Therefore, in this paper, a routing protocol for HWSNs based on the modified grey wolf optimizer (HMGWO) is proposed. First, the protocol selects the appropriate initial clusters by defining different fitness functions for heterogeneous energy nodes; the nodes\u2019 fitness values are then calculated and treated as initial weights in the GWO. At the same time, the weights are dynamically updated according to the distance between the wolves and their prey and coefficient vectors to improve the GWO\u2019s optimization ability and ensure the selection of the optimal cluster heads (CHs). The experimental results indicate that the network lifecycle of the HMGWO protocol improves by 55.7%, 31.9%, 46.3%, and 27.0%, respectively, compared with the stable election protocol (SEP), distributed energy-efficient clustering algorithm (DEEC), modified SEP (M-SEP), and fitness-value-based improved GWO (FIGWO) protocols. In terms of the power consumption and network throughput, the HMGWO is also superior to other protocols.<\/jats:p>","DOI":"10.3390\/s20030820","type":"journal-article","created":{"date-parts":[[2020,2,5]],"date-time":"2020-02-05T03:18:48Z","timestamp":1580872728000},"page":"820","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":56,"title":["Routing Protocol for Heterogeneous Wireless Sensor Networks Based on a Modified Grey Wolf Optimizer"],"prefix":"10.3390","volume":"20","author":[{"given":"Xiaoqiang","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Communication and Information Engineering, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an 710121, China"},{"name":"Shaanxi Key Laboratory of Information Communication Network and Security, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an 710121, China"}]},{"given":"Shaoya","family":"Ren","sequence":"additional","affiliation":[{"name":"School of Communication and Information Engineering, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an 710121, China"},{"name":"Shaanxi Key Laboratory of Information Communication Network and Security, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an 710121, China"}]},{"given":"Heng","family":"Quan","sequence":"additional","affiliation":[{"name":"School of Communication and Information Engineering, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an 710121, China"},{"name":"Shaanxi Key Laboratory of Information Communication Network and Security, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an 710121, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1785-987X","authenticated-orcid":false,"given":"Qiang","family":"Gao","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electronic Engineering, Northwest Agriculture and Forestry University, Yangling 712100, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,4]]},"reference":[{"key":"ref_1","unstructured":"Ramson, S.R.J., and Moni, D.J. (2017, January 3\u20134). Applications of wireless sensor networks\u2014A survey. Proceedings of the 2017 International Conference on Innovations in Electrical, Electronics, Instrumentation and Media Technology (ICEEIMT), Coimbatore, India."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.jnca.2015.09.008","article-title":"Applications of wireless sensor networks for urban areas: A survey","volume":"60","author":"Rashid","year":"2016","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1108\/SR-08-2014-683","article-title":"Recent trend in wireless sensor network and its applications: A survey","volume":"35","author":"Prasad","year":"2015","journal-title":"Sens. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ransing, R.S., and Rajput, M. (2015, January 9\u201310). Smart home for elderly care, based on Wireless Sensor Network. Proceedings of the 2015 International Conference on Nascent Technologies in the Engineering Field (ICNTE), Navi Mumbai, India.","DOI":"10.1109\/ICNTE.2015.7029932"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.compag.2015.08.011","article-title":"Wireless sensor networks for agriculture: The state-of-the-art in practice and future challenges","volume":"118","author":"Ojha","year":"2015","journal-title":"Comput. Electron. Agric."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1109\/MCOM.2002.1024422","article-title":"A survey on sensor networks","volume":"40","author":"Akyildiz","year":"2002","journal-title":"IEEE Commun. Mag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2292","DOI":"10.1016\/j.comnet.2008.04.002","article-title":"Wireless sensor network survey","volume":"52","author":"Yick","year":"2008","journal-title":"Comput. Netw."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1007\/s11277-018-5747-9","article-title":"Survey on Wireless Sensor Network Applications and Energy Efficient Routing Protocols","volume":"101","author":"Mohamed","year":"2018","journal-title":"Wireless Pers. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1084","DOI":"10.3390\/s17051084","article-title":"A Survey on an Energy-Efficient and Energy-Balanced Routing Protocol for Wireless Sensor Networks","volume":"17","author":"Olayinka","year":"2017","journal-title":"Sensors"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhao, Z., Xu, K., Hui, G., and Hu, L. (2018). An Energy-Efficient Clustering Routing Protocol for Wireless Sensor Networks Based on AGNES with Balanced Energy Consumption Optimization. Sensors, 18.","DOI":"10.3390\/s18113938"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hosen, A., and Gi, C. (2018). An Energy Centric Cluster-Based Routing Protocol for Wireless Sensor Networks. Sensors, 18.","DOI":"10.3390\/s18051520"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Liu, X. (2012). A Survey on Clustering Routing Protocols in Wireless Sensor Networks. Sensors, 12.","DOI":"10.3390\/s120811113"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1016\/j.procs.2015.03.133","article-title":"A Survey on Cluster Based Routing Protocols in Wireless Sensor Networks","volume":"45","author":"Singh","year":"2015","journal-title":"Procedia Comput. Sci."},{"key":"ref_14","unstructured":"Heinzelman, W.R., Chandrakasan, A., and Balakrishnan, H. (2000, January 7). Energy-Efficient Communication Protocol for Wireless Microsensor Networks. Proceedings of the 33rd Annual Hawaii International Conference on System Sciences, Maui, HI, USA."},{"key":"ref_15","unstructured":"Manjeshwar, A., and Agrawal, D.P. (2001, January 23\u201327). TEEN: A Routing Protocol for Enhanced Efficiency in Wireless Sensor Networks. Proceedings of the 15th International Parallel and Distributed Processing Symposium, San Francisco, CA, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1109\/TMC.2004.41","article-title":"HEED: A hybrid, energy-efficient, distributed clustering approach for ad hoc sensor networks","volume":"3","author":"Younis","year":"2004","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.protcy.2012.05.024","article-title":"Clustering in wireless sensor networks: Performance comparison of LEACH & LEACH-C protocols using ns2","volume":"4","author":"Geetha","year":"2012","journal-title":"Procedia Technol."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Ducrocq, T., Mitton, N., and Hauspie, M. (2013, January 7\u201310). Energy-based clustering for wireless sensor network lifetime optimization. Proceedings of the 2013 IEEE Wireless Communications and Networking Conference (WCNC), Shanghai, China.","DOI":"10.1109\/WCNC.2013.6554695"},{"key":"ref_19","first-page":"1","article-title":"VCH-ECCR: A Centralized Routing Protocol for Wireless Sensor Networks","volume":"1","author":"Rohit","year":"2017","journal-title":"J. Sens."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Hamzah, A., Shurman, M., Al-Jarrah, O., and Taqieddin, E. (2019). Energy-Efficient Fuzzy-Logic-Based Clustering Technique for Hierarchical Routing Protocols in Wireless Sensor Networks. Sensors, 19.","DOI":"10.3390\/s19030561"},{"key":"ref_21","unstructured":"Smaragdakis, G., Matta, I., and Bestavros, A. (2004, January 22). SEP: A stable election protocol for clustered heterogeneous wireless sensor networks. Proceedings of the 2nd International Workshop on Sensor and Actor Network Protocols and Applications, Boston, MA, USA."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Singh, D., and Panda, C.K. (2015, January 24\u201325). Performance analysis of Modified Stable Election Protocol in heterogeneous WSN. Proceedings of the 2015 International Conference on Electrical, Electronics, Signals, Communication and Optimization (EESCO), Visakhapatnam, India.","DOI":"10.1109\/EESCO.2015.7253803"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1007\/s11227-016-1785-9","article-title":"P-SEP: A prolong stable election routing algorithm for energy-limited heterogeneous fog-supported wireless sensor networks","volume":"73","author":"Naranjo","year":"2017","journal-title":"J. Supercomput."},{"key":"ref_24","first-page":"1050","article-title":"An improved energy aware distributed unequal clustering protocol for heterogeneous wireless sensor networks","volume":"19","author":"Gupta","year":"2016","journal-title":"Eng. Sci. Technol. Int. J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2230","DOI":"10.1016\/j.comcom.2006.02.017","article-title":"Design of a distributed energy-efficient clustering algorithm for heterogeneous wireless sensor network","volume":"29","author":"Qing","year":"2006","journal-title":"Comput. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/s11235-017-0372-6","article-title":"An unequal cluster-based routing scheme for multi-level heterogeneous wireless sensor networks","volume":"68","author":"Yang","year":"2018","journal-title":"Telecommun. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Bhushan, S., Pal, R., and Antoshchuk, S.G. (2018, January 21\u201325). Energy Efficient Clustering Protocol for Heterogeneous Wireless Sensor Network: A Hybrid Approach Using GA and K-means. Proceedings of the 2018 IEEE Second International Conference on Data Stream Mining & Processing (DSMP), Lviv, Ukraine.","DOI":"10.1109\/DSMP.2018.8478538"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1108\/SR-06-2016-0104","article-title":"A survey on clustering routing protocols in wireless sensor networks","volume":"37","author":"Gherbi","year":"2017","journal-title":"Sens. Rev."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Mazumdar, N., Roy, S., and Nayak, S. (2018, January 21\u201323). A Survey on Clustering Approaches for Wireless Sensor Networks. Proceedings of the 2018 2nd International Conference on Data Science and Business Analytics (ICDSBA), Changsha, China.","DOI":"10.1109\/ICDSBA.2018.00049"},{"key":"ref_30","unstructured":"Tong, M., and Tang, M. (2010, January 23\u201325). LEACH-B: An Improved LEACH Protocol for Wireless Sensor Network. Proceedings of the 2010 6th International Conference on Wireless Communications Networking and Mobile Computing (WiCOM), Chengdu, China."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1415","DOI":"10.1007\/s11276-015-1063-4","article-title":"An energy efficient routing protocol for correlated data using CL-LEACH in WSN","volume":"22","author":"Marappan","year":"2015","journal-title":"Wirel. Netw."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Razaque, A., Mudigulam, S., Gavini, K., Amsaad, F., Abdulgader, M., and Krishna, G.S. (2016, January 29\u201329). H-LEACH: Hybrid-low energy adaptive clustering hierarchy for wireless sensor networks. Proceedings of the 2016 IEEE Long Island Systems, Applications and Technology Conference (LISAT), Farmingdale, NY, USA.","DOI":"10.1109\/LISAT.2016.7494136"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Jerbi, W., Guermazi, A., and Trabelsi, H. (April, January 29). O-LEACH of Routing Protocol for Wireless Sensor Networks. Proceedings of the 2016 13th International Conference on Computer Graphics, Imaging and Visualization (CGiV), Beni Mellal, Morocco.","DOI":"10.1109\/CGiV.2016.84"},{"key":"ref_34","first-page":"1","article-title":"An information entropy based-clustering algorithm for heterogeneous wireless sensor networks","volume":"12","author":"Osamy","year":"2018","journal-title":"Wirel. Netw."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1477","DOI":"10.1007\/s11277-018-5649-x","article-title":"Cluster-Head Restricted Energy Efficient Protocol (CREEP) for Routing in Heterogeneous Wireless Sensor Networks","volume":"100","author":"Dutt","year":"2018","journal-title":"Wirel. Pers. Commun."},{"key":"ref_36","first-page":"2078627","article-title":"Energy Efficient Clustering Protocol to Enhance Performance of Heterogeneous Wireless Sensor Network: EECPEP-HWSN","volume":"2018","author":"Purkar","year":"2018","journal-title":"J. Comput. Netw. Commun."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Zhao, X., Cui, Y., Guo, Z., and Hao, Z. (2020). An Energy-Efficient Coverage Enhancement Strategy for Wireless Sensor Networks Based on a Dynamic Partition Algorithm for Cellular Grids and an Improved Vampire Bat Optimizer. Sensors, 20.","DOI":"10.3390\/s20030619"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1109\/JIOT.2019.2952718","article-title":"Energy-efficient Coverage Enhancement Strategy for Three-dimensional Wireless Sensor Networks Based on a Vampire Bat Optimizer","volume":"7","author":"Zhao","year":"2020","journal-title":"IEEE Internet Things J."},{"key":"ref_39","first-page":"1","article-title":"On-demand fuzzy clustering and ant-colony optimisation based mobile data collection in wireless sensor network","volume":"8","author":"Nimisha","year":"2017","journal-title":"Wirel. Netw."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1007\/s11235-017-0348-6","article-title":"An energy-aware routing protocol for wireless sensor network based on genetic algorithm","volume":"67","author":"Kong","year":"2018","journal-title":"Telecommun. Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1016\/j.asej.2016.03.004","article-title":"Lifetime Improvement in Wireless Sensor Networks using Hybrid Differential Evolution and Simulated Annealing (DESA)","volume":"9","author":"Sweta","year":"2018","journal-title":"Ain Shams Eng. J."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2633","DOI":"10.1007\/s11277-017-4627-z","article-title":"Cluster Optimization Based on Metaheuristic Algorithms in Wireless Sensor Networks","volume":"97","author":"Mekonnen","year":"2017","journal-title":"Wirel. Pers. Commun."},{"key":"ref_43","first-page":"286","article-title":"SAT: Simulated Annealing and Tabu Search Based Routing Algorithm for Wireless Sensor Networks","volume":"4","author":"Mohammadi","year":"2016","journal-title":"Int. J. Comput. Netw. Commun. Secur."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"129","DOI":"10.3991\/ijoe.v15i01.9784","article-title":"Clustering and Path Planning for Wireless Sensor Networks Based on Improved Ant Colony Algorithm","volume":"15","author":"Fang","year":"2019","journal-title":"Int. J. Online Biomed. Eng."},{"key":"ref_45","first-page":"71","article-title":"A Clustering Routing Protocol for Energy Balance of Wireless Sensor Network based on Simulated Annealing and Genetic Algorithm","volume":"7","author":"Zhang","year":"2014","journal-title":"Int. J. Hybrid Inf. Technol."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Wang, J., Gao, Y., Liu, W., Sangaiah, A.K., and Kim, H.J. (2019). An Improved Routing Schema with Special Clustering Using PSO Algorithm for Heterogeneous Wireless Sensor Network. Sensors, 19.","DOI":"10.3390\/s19030671"},{"key":"ref_47","first-page":"1","article-title":"Genetic-Algorithm-Based Energy-Efficient Clustering (GAEEC) for Homogenous Wireless Sensor Networks","volume":"64","author":"Singh","year":"2017","journal-title":"IETE J. Res."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Al-Aboody, N.A., and Al-Raweshidy, H.S. (2016, January 5\u20137). Grey wolf optimization-based energy-efficient routing protocol for heterogeneous wireless sensor networks. Proceedings of the 2016 4th International Symposium on Computational and Business Intelligence (ISCBI), Olten, Switzerland.","DOI":"10.1109\/ISCBI.2016.7743266"},{"key":"ref_49","first-page":"2644","article-title":"Energy-Efficient Routing Protocol for Wireless Sensor Networks Based on Improved Grey Wolf Optimizer","volume":"12","author":"Zhao","year":"2018","journal-title":"KSII T. Internet Inf."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","article-title":"Grey Wolf Optimizer","volume":"69","author":"Mirjalili","year":"2014","journal-title":"Adv. Eng. Softw."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1109\/TWC.2002.804190","article-title":"An application-specific protocol architecturefor wireless microsensor networks","volume":"1","author":"Heinzelman","year":"2002","journal-title":"IEEE Trans. Wirel. Commun."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/3\/820\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:54:21Z","timestamp":1760172861000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/3\/820"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,4]]},"references-count":51,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["s20030820"],"URL":"https:\/\/doi.org\/10.3390\/s20030820","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,4]]}}}